{"product_id":"numerical-calculations-in-clifford-algebra-isbn-9781394173242","title":"Numerical Calculations in Clifford Algebra","description":"\u003cb\u003eNUMERICAL CALCULATIONS IN CLIFFORD ALGEBRA\u003c\/b\u003e \u003cp\u003e\u003cb\u003eAn intuitive combination of the theory of Clifford algebra with numerous worked and computed examples and calculations\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\u003ci\u003eNumerical Calculations in Clifford Algebra: A Practical Guide for Engineers and Scientists\u003c\/i\u003e is an accessible and practical introduction to Clifford algebra, with comprehensive coverage of the theory and calculations. The book offers many worked and computed examples at a variety of levels of complexity and over a range of different applications making extensive use of diagrams to maintain clarity. The author introduces and documents the Clifford Numerical Suite, developed to overcome the limitations of existing computational packages and to enable the rapid creation and deployment of sophisticated and efficient code. \u003c\/p\u003e\u003cp\u003eApplications of the suite include Fourier transforms for arrays of any types of Clifford numbers and the solution of linear systems in which the coefficients are Clifford numbers of particular types, including scalars, bicomplex numbers, quaternions, Pauli matrices, and extended electromagnetic fields. Readers will find: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eA thorough introduction to Clifford algebra, with a combination of theory and practical implementation in a range of engineering problems\u003c\/li\u003e \u003cli\u003eComprehensive explorations of a variety of worked and computed examples at various levels of complexity\u003c\/li\u003e \u003cli\u003ePractical discussions of the conceptual and computational tools for solving common engineering problems\u003c\/li\u003e \u003cli\u003eDetailed documentation on the deployment and application of the Clifford Numerical Suite\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003ePerfect for engineers, researchers, and academics with an interest in Clifford algebra, \u003ci\u003eNumerical Calculations in Clifford Algebra: A Practical Guide for Engineers and Scientists\u003c\/i\u003e will particularly benefit professionals in the areas of antenna design, digital image processing, theoretical physics, and geometry. \u003c\/p\u003e\u003cp\u003eList of Figures xv\u003c\/p\u003e \u003cp\u003eList of Tables xix\u003c\/p\u003e \u003cp\u003ePreface xxi\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Entities and Operations 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Operations 3\u003c\/p\u003e \u003cp\u003e1.2 History 4\u003c\/p\u003e \u003cp\u003e1.3 Alternative Forms 5\u003c\/p\u003e \u003cp\u003e1.4 Naming 6\u003c\/p\u003e \u003cp\u003e1.5 Structure 7\u003c\/p\u003e \u003cp\u003e1.5.1 Algebraic 7\u003c\/p\u003e \u003cp\u003e1.5.2 Numeric 8\u003c\/p\u003e \u003cp\u003e1.6 Entities 11\u003c\/p\u003e \u003cp\u003eReferences 12\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Input 13\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Syntax 13\u003c\/p\u003e \u003cp\u003e2.2 Constants 14\u003c\/p\u003e \u003cp\u003e2.2.1 Specific Types 14\u003c\/p\u003e \u003cp\u003e2.2.2 General 16\u003c\/p\u003e \u003cp\u003e2.3 Variables 19\u003c\/p\u003e \u003cp\u003e2.3.1 Checking and Converting 19\u003c\/p\u003e \u003cp\u003eReference 23\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Output 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Tree Format 26\u003c\/p\u003e \u003cp\u003e3.2 Numeric Formats 29\u003c\/p\u003e \u003cp\u003e3.2.1 Default Format 29\u003c\/p\u003e \u003cp\u003e3.2.2 Defined Format 31\u003c\/p\u003e \u003cp\u003e3.3 Extended Formats 32\u003c\/p\u003e \u003cp\u003e3.3.1 Rounding 32\u003c\/p\u003e \u003cp\u003e3.3.2 Parts of Coefficients 33\u003c\/p\u003e \u003cp\u003e3.4 Selected Components 35\u003c\/p\u003e \u003cp\u003e3.5 Primitive Formats 36\u003c\/p\u003e \u003cp\u003e3.6 Recovered Values 38\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Unary Operations 41\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Theory 41\u003c\/p\u003e \u003cp\u003e4.1.1 Negation 41\u003c\/p\u003e \u003cp\u003e4.1.2 Involution 41\u003c\/p\u003e \u003cp\u003e4.1.3 Pair Exchange 42\u003c\/p\u003e \u003cp\u003e4.1.4 Reversion 43\u003c\/p\u003e \u003cp\u003e4.1.5 Clifford Conjugation 44\u003c\/p\u003e \u003cp\u003e4.1.6 Supplementation and Pseudo-scalar 44\u003c\/p\u003e \u003cp\u003e4.2 Practice 45\u003c\/p\u003e \u003cp\u003e4.2.1 Example Code 45\u003c\/p\u003e \u003cp\u003e4.2.2 Example Output 47\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Binary Operations 49\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Geometric Origins 49\u003c\/p\u003e \u003cp\u003e5.1.1 Outer Multiplication 49\u003c\/p\u003e \u003cp\u003e5.1.2 Orthogonal Components 52\u003c\/p\u003e \u003cp\u003e5.1.3 Inner Multiplication 53\u003c\/p\u003e \u003cp\u003e5.1.4 Names 54\u003c\/p\u003e \u003cp\u003e5.2 Multiplication of Units 55\u003c\/p\u003e \u003cp\u003e5.2.1 Progressive and Regressive Multiplication 55\u003c\/p\u003e \u003cp\u003e5.2.2 Outer, Inner, and Central Multiplication 57\u003c\/p\u003e \u003cp\u003e5.2.3 Multiplication By Scalars 58\u003c\/p\u003e \u003cp\u003e5.3 Central Multiplication 59\u003c\/p\u003e \u003cp\u003e5.3.1 Primal Units 60\u003c\/p\u003e \u003cp\u003e5.3.2 Evolved and Other Units 61\u003c\/p\u003e \u003cp\u003e5.3.3 Numbers 62\u003c\/p\u003e \u003cp\u003e5.4 Practice 63\u003c\/p\u003e \u003cp\u003e5.4.1 Example Code 63\u003c\/p\u003e \u003cp\u003e5.4.2 Example Output 65\u003c\/p\u003e \u003cp\u003e5.4.3 Multiplication Tables 65\u003c\/p\u003e \u003cp\u003eReferences 70\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Vectors and Geometry 71\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Theory 71\u003c\/p\u003e \u003cp\u003e6.1.1 Magnitude 71\u003c\/p\u003e \u003cp\u003e6.1.2 Inverse 72\u003c\/p\u003e \u003cp\u003e6.1.3 Reflection 72\u003c\/p\u003e \u003cp\u003e6.1.4 Projection 73\u003c\/p\u003e \u003cp\u003e6.1.5 Rotation 73\u003c\/p\u003e \u003cp\u003e6.2 Practice 74\u003c\/p\u003e \u003cp\u003e6.2.1 Example Code 74\u003c\/p\u003e \u003cp\u003e6.2.2 Example Output 76\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Quaternions 79\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Theory 79\u003c\/p\u003e \u003cp\u003e7.1.1 Magnitude 80\u003c\/p\u003e \u003cp\u003e7.1.2 Inverse 80\u003c\/p\u003e \u003cp\u003e7.1.3 Reflection and Projection 80\u003c\/p\u003e \u003cp\u003e7.1.4 Rotation 81\u003c\/p\u003e \u003cp\u003e7.1.5 Intersection 82\u003c\/p\u003e \u003cp\u003e7.1.6 Factorisation 82\u003c\/p\u003e \u003cp\u003e7.2 Practice 83\u003c\/p\u003e \u003cp\u003e7.2.1 Example Code 83\u003c\/p\u003e \u003cp\u003e7.2.2 Example Output 86\u003c\/p\u003e \u003cp\u003eReferences 87\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Pauli Matrices 89\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Theory 89\u003c\/p\u003e \u003cp\u003e8.1.1 Recovery of Components 90\u003c\/p\u003e \u003cp\u003e8.1.2 Magnitude 90\u003c\/p\u003e \u003cp\u003e8.1.3 Inverse 91\u003c\/p\u003e \u003cp\u003e8.1.4 Reflection, Projection, and Rotation 91\u003c\/p\u003e \u003cp\u003e8.2 Practice 91\u003c\/p\u003e \u003cp\u003e8.2.1 Example Code 91\u003c\/p\u003e \u003cp\u003e8.2.2 Example Output 94\u003c\/p\u003e \u003cp\u003eReference 95\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Bicomplex Numbers 97\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Theory 97\u003c\/p\u003e \u003cp\u003e9.1.1 Conjugate 98\u003c\/p\u003e \u003cp\u003e9.1.2 Magnitude 98\u003c\/p\u003e \u003cp\u003e9.1.3 Inverse 98\u003c\/p\u003e \u003cp\u003e9.1.4 Reflection, Projection, and Rotation 99\u003c\/p\u003e \u003cp\u003e9.2 Practice 99\u003c\/p\u003e \u003cp\u003e9.2.1 Example Code 99\u003c\/p\u003e \u003cp\u003e9.2.2 Example Output 101\u003c\/p\u003e \u003cp\u003eReference 102\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Electromagnetic Fields 103\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Theory 103\u003c\/p\u003e \u003cp\u003e10.1.1 Time and Frequency 103\u003c\/p\u003e \u003cp\u003e10.1.2 Electromagnetic Entities 104\u003c\/p\u003e \u003cp\u003e10.1.3 Dirac Operators 105\u003c\/p\u003e \u003cp\u003e10.1.4 Maxwell’s Equations 105\u003c\/p\u003e \u003cp\u003e10.1.5 Simplified Notation 105\u003c\/p\u003e \u003cp\u003e10.1.6 Magnitude 106\u003c\/p\u003e \u003cp\u003e10.1.7 Inverse 106\u003c\/p\u003e \u003cp\u003e10.1.8 Reflection 107\u003c\/p\u003e \u003cp\u003e10.1.9 Projection 107\u003c\/p\u003e \u003cp\u003e10.1.10 Rotation 107\u003c\/p\u003e \u003cp\u003e10.2 Practice 107\u003c\/p\u003e \u003cp\u003e10.2.1 Example Code 107\u003c\/p\u003e \u003cp\u003e10.2.2 Example Output 110\u003c\/p\u003e \u003cp\u003e10.3 Field Arithmetic 112\u003c\/p\u003e \u003cp\u003e10.3.1 Extensions Based on Quaternions 112\u003c\/p\u003e \u003cp\u003e10.3.2 Inverses 113\u003c\/p\u003e \u003cp\u003e10.3.3 Example Code 115\u003c\/p\u003e \u003cp\u003e10.3.4 Example Output 117\u003c\/p\u003e \u003cp\u003eReferences 118\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Arrays of Clifford Numbers 119\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Theory 119\u003c\/p\u003e \u003cp\u003e11.2 Practice 120\u003c\/p\u003e \u003cp\u003e11.2.1 Example Code 120\u003c\/p\u003e \u003cp\u003e11.2.2 Example Output 123\u003c\/p\u003e \u003cp\u003eReference 125\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Power Series 127\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Theory 127\u003c\/p\u003e \u003cp\u003e12.1.1 User Defined 127\u003c\/p\u003e \u003cp\u003e12.1.2 Predefined 128\u003c\/p\u003e \u003cp\u003e12.1.3 Convergence 129\u003c\/p\u003e \u003cp\u003e12.1.4 Factorisation 130\u003c\/p\u003e \u003cp\u003e12.1.5 Squaring 131\u003c\/p\u003e \u003cp\u003e12.2 Practice 131\u003c\/p\u003e \u003cp\u003e12.2.1 User Defined 131\u003c\/p\u003e \u003cp\u003e12.2.2 Predefined 133\u003c\/p\u003e \u003cp\u003e12.2.2.1 Standard Convergence 136\u003c\/p\u003e \u003cp\u003e12.2.2.2 Extended Convergence 141\u003c\/p\u003e \u003cp\u003e12.2.2.3 Doubly Extended Convergence 146\u003c\/p\u003e \u003cp\u003eReferences 148\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Matrices of Clifford Numbers 149\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Background 149\u003c\/p\u003e \u003cp\u003e13.2 Inversion 150\u003c\/p\u003e \u003cp\u003e13.3 Practice 152\u003c\/p\u003e \u003cp\u003e13.3.1 Example Code 152\u003c\/p\u003e \u003cp\u003e13.3.2 Example Output 155\u003c\/p\u003e \u003cp\u003eReference 159\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Customisation 161\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Memory 163\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Memory Usage 163\u003c\/p\u003e \u003cp\u003e14.2 Examples 165\u003c\/p\u003e \u003cp\u003e14.2.1 Memory Tree Sparsity 165\u003c\/p\u003e \u003cp\u003e14.2.2 Memory Expansion 170\u003c\/p\u003e \u003cp\u003e14.2.3 Memory Recycling 171\u003c\/p\u003e \u003cp\u003e14.2.3.1 Explicit and Implicit 171\u003c\/p\u003e \u003cp\u003e14.2.3.2 Implicit and Nested 173\u003c\/p\u003e \u003cp\u003eReference 175\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Errors 177\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 User Errors 177\u003c\/p\u003e \u003cp\u003e15.1.1 Syntax Errors and Messages 180\u003c\/p\u003e \u003cp\u003e15.2 System Errors 181\u003c\/p\u003e \u003cp\u003e15.3 Recovery 182\u003c\/p\u003e \u003cp\u003e15.4 Beneficial Usage 185\u003c\/p\u003e \u003cp\u003eReference 191\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Extension 193\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Accumulation 193\u003c\/p\u003e \u003cp\u003e16.2 Multiplication 195\u003c\/p\u003e \u003cp\u003e16.3 Transformation 197\u003c\/p\u003e \u003cp\u003e16.4 Filtration 198\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Application 203\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Verification 205\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Identities 205\u003c\/p\u003e \u003cp\u003e17.2 Tests 205\u003c\/p\u003e \u003cp\u003e17.2.1 Example Code 205\u003c\/p\u003e \u003cp\u003e17.2.2 Example Output 208\u003c\/p\u003e \u003cp\u003eReference 214\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Lines Not Parallel 215\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Theory 215\u003c\/p\u003e \u003cp\u003e18.1.1 Common Plane 215\u003c\/p\u003e \u003cp\u003e18.1.1.1 Inner Product 216\u003c\/p\u003e \u003cp\u003e18.1.1.2 Outer Product 217\u003c\/p\u003e \u003cp\u003e18.1.1.3 Geometrical Interpretation 217\u003c\/p\u003e \u003cp\u003e18.1.2 No Plane in Common 218\u003c\/p\u003e \u003cp\u003e18.1.2.1 Inner Product 219\u003c\/p\u003e \u003cp\u003e18.1.2.2 Solution 219\u003c\/p\u003e \u003cp\u003e18.2 Practice 220\u003c\/p\u003e \u003cp\u003e18.2.1 Example Code 220\u003c\/p\u003e \u003cp\u003e18.2.2 Example Output 223\u003c\/p\u003e \u003cp\u003eReference 224\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Perspective Projection 225\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Theory 225\u003c\/p\u003e \u003cp\u003e19.2 Practice 225\u003c\/p\u003e \u003cp\u003e19.2.1 Example Code 225\u003c\/p\u003e \u003cp\u003e19.2.2 Example Output 229\u003c\/p\u003e \u003cp\u003eReference 230\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Linear Systems 231\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e20.1 Theory 231\u003c\/p\u003e \u003cp\u003e20.2 Practice 233\u003c\/p\u003e \u003cp\u003e20.2.1 Example Code 233\u003c\/p\u003e \u003cp\u003e20.2.2 Example Output 235\u003c\/p\u003e \u003cp\u003eReferences 235\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 Fast Fourier Transform 237\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e21.1 Theory 237\u003c\/p\u003e \u003cp\u003e21.2 Practice 238\u003c\/p\u003e \u003cp\u003e21.2.1 Example Code 238\u003c\/p\u003e \u003cp\u003e21.2.2 Example Output 243\u003c\/p\u003e \u003cp\u003eReferences 244\u003c\/p\u003e \u003cp\u003e\u003cb\u003e22 Hertzian Dipole 245\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e22.1 Theory 245\u003c\/p\u003e \u003cp\u003e22.2 Practice 246\u003c\/p\u003e \u003cp\u003e22.2.1 Example Code 246\u003c\/p\u003e \u003cp\u003e22.2.2 Example Output 251\u003c\/p\u003e \u003cp\u003eReference 253\u003c\/p\u003e \u003cp\u003e\u003cb\u003e23 Finite Difference Time Domain 255\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e23.1 Theory 255\u003c\/p\u003e \u003cp\u003e23.1.1 Analytical Solution 255\u003c\/p\u003e \u003cp\u003e23.1.2 Series Solution 256\u003c\/p\u003e \u003cp\u003e23.1.3 Analytical Example 257\u003c\/p\u003e \u003cp\u003e23.1.4 Numerical Derivatives 257\u003c\/p\u003e \u003cp\u003e23.2 Practice 259\u003c\/p\u003e \u003cp\u003e23.2.1 Example Code 259\u003c\/p\u003e \u003cp\u003e23.2.2 Example Output 265\u003c\/p\u003e \u003cp\u003eReferences 270\u003c\/p\u003e \u003cp\u003e\u003cb\u003e24 Cauchy Extension 271\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e24.1 Background 271\u003c\/p\u003e \u003cp\u003e24.2 Theory 272\u003c\/p\u003e \u003cp\u003e24.2.1 Two Dimensions 272\u003c\/p\u003e \u003cp\u003e24.2.2 Three Dimensions 272\u003c\/p\u003e \u003cp\u003e24.2.3 Singularity 273\u003c\/p\u003e \u003cp\u003e24.2.4 The Taming Function 273\u003c\/p\u003e \u003cp\u003e24.2.5 Construction 274\u003c\/p\u003e \u003cp\u003e24.3 Practice 276\u003c\/p\u003e \u003cp\u003e24.3.1 Example Code 276\u003c\/p\u003e \u003cp\u003e24.3.2 Example Output 281\u003c\/p\u003e \u003cp\u003eReferences 284\u003c\/p\u003e \u003cp\u003e\u003cb\u003e25 Electromagnetic Scattering 285\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e25.1 Background 285\u003c\/p\u003e \u003cp\u003e25.2 Theory 286\u003c\/p\u003e \u003cp\u003e25.3 Practice 288\u003c\/p\u003e \u003cp\u003e25.3.1 Example Code 288\u003c\/p\u003e \u003cp\u003e25.3.2 Example Output 289\u003c\/p\u003e \u003cp\u003eReferences 293\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV Programming 295\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e26 Interfaces 297\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e26.1 Configuration and Observation 297\u003c\/p\u003e \u003cp\u003e26.1.1 Management 297\u003c\/p\u003e \u003cp\u003e26.1.2 Printing 298\u003c\/p\u003e \u003cp\u003e26.2 Simple Entities 300\u003c\/p\u003e \u003cp\u003e26.2.1 Units 300\u003c\/p\u003e \u003cp\u003e26.2.2 Components 300\u003c\/p\u003e \u003cp\u003e26.2.3 Numbers 302\u003c\/p\u003e \u003cp\u003e26.2.3.1 Establishing and Recovering Values 302\u003c\/p\u003e \u003cp\u003e26.2.3.2 Functions 303\u003c\/p\u003e \u003cp\u003e26.2.3.3 Addition and Subtraction 304\u003c\/p\u003e \u003cp\u003e26.2.3.4 Multiplication 304\u003c\/p\u003e \u003cp\u003e26.2.3.5 Geometric 305\u003c\/p\u003e \u003cp\u003e26.2.3.6 Filtering 305\u003c\/p\u003e \u003cp\u003e26.3 Higher Entities 306\u003c\/p\u003e \u003cp\u003e26.3.1 Vectors 306\u003c\/p\u003e \u003cp\u003e26.3.2 Bicomplex Numbers 307\u003c\/p\u003e \u003cp\u003e26.3.3 Quaternions 307\u003c\/p\u003e \u003cp\u003e26.3.4 Pauli Matrices 308\u003c\/p\u003e \u003cp\u003e26.3.5 Electromagnetic Fields 308\u003c\/p\u003e \u003cp\u003e26.4 Multiple Entities 309\u003c\/p\u003e \u003cp\u003e26.4.1 Arrays 309\u003c\/p\u003e \u003cp\u003e26.4.2 Fast Fourier Transforms 309\u003c\/p\u003e \u003cp\u003e26.4.3 Series 310\u003c\/p\u003e \u003cp\u003e26.4.4 Matrices 310\u003c\/p\u003e \u003cp\u003eReference 311\u003c\/p\u003e \u003cp\u003e\u003cb\u003e27 Descriptions 313\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e27.1 Arguments 313\u003c\/p\u003e \u003cp\u003e27.2 Data types 313\u003c\/p\u003e \u003cp\u003e27.3 Formats 315\u003c\/p\u003e \u003cp\u003e27.4 Manual Pages 316\u003c\/p\u003e \u003cp\u003e27.4.1 A–e 316\u003c\/p\u003e \u003cp\u003e27.4.2 F–j 342\u003c\/p\u003e \u003cp\u003e27.4.3 K–o 369\u003c\/p\u003e \u003cp\u003e27.4.4 P–t 387\u003c\/p\u003e \u003cp\u003e27.4.5 U–z 468\u003c\/p\u003e \u003cp\u003e27.5 Quick Reference 477\u003c\/p\u003e \u003cp\u003eReference 487\u003c\/p\u003e \u003cp\u003eA Key to Example Code and Results 489\u003c\/p\u003e \u003cp\u003eIndex 493\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eAndrew Seagar, PhD,\u003c\/b\u003e is Director for the Bachelor of Engineering Programs at the Gold Coast Campus of the School of Engineering at Griffith University in Australia. He has experience in a variety of research, commercial development, and academic positions around the world, primarily in the areas of electrical or biomedical engineering.   \u003c\/p\u003e\u003cp\u003e\u003cb\u003eAn intuitive combination of the theory of Clifford algebra with numerous worked and computed examples and calculations\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003e\u003ci\u003eNumerical Calculations in Clifford Algebra: A Practical Guide for Engineers and Scientists\u003c\/i\u003e is an accessible and practical introduction to Clifford algebra, with comprehensive coverage of the theory and calculations. The book offers many worked and computed examples at a variety of levels of complexity and over a range of different applications making extensive use of diagrams to maintain clarity. The author introduces and documents the Clifford Numerical Suite, developed to overcome the limitations of existing computational packages and to enable the rapid creation and deployment of sophisticated and efficient code. \u003c\/p\u003e\u003cp\u003eApplications of the suite include Fourier transforms for arrays of any types of Clifford numbers and the solution of linear systems in which the coefficients are Clifford numbers of particular types, including scalars, bicomplex numbers, quaternions, Pauli matrices, and extended electromagnetic fields. Readers will find: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eA thorough introduction to Clifford algebra, with a combination of theory and practical implementation in a range of engineering problems\u003c\/li\u003e \u003cli\u003eComprehensive explorations of a variety of worked and computed examples at various levels of complexity\u003c\/li\u003e \u003cli\u003ePractical discussions of the conceptual and computational tools for solving common engineering problems\u003c\/li\u003e \u003cli\u003eDetailed documentation on the deployment and application of the Clifford Numerical Suite\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003ePerfect for engineers, researchers, and academics with an interest in Clifford algebra, \u003ci\u003eNumerical Calculations in Clifford Algebra: A Practical Guide for Engineers and Scientists\u003c\/i\u003e will particularly benefit professionals in the areas of antenna design, digital image processing, theoretical physics, and geometry.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989702263013,"sku":"NP9781394173242","price":120.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781394173242.jpg?v=1761785166","url":"https:\/\/k12savings.com\/es\/products\/numerical-calculations-in-clifford-algebra-isbn-9781394173242","provider":"K12savings","version":"1.0","type":"link"}